OP, let me lay it out for you. It comes in a succession of logical pieces:
You have to look at the orientation of the horse’s ribcage, his carcass, basically. Is that tilted uphill? How uphill? Can you see his withers being higher than his croup? Can you see his croup being lowered? Is rib cage flat? Is it even downhill?
The neck–let’s say from the base where it comes out of his shoulders to just about his throatlatch— have to be in a position that relate to the orientation of his rib cage. That’s it. The orientation of the rib cage is the only reason the position of the neck matters.
The throat latch-- that last final hinge at the top of the neck-- also doesn’t matter, except as it tends to stay open or closed in a way that is determined by the rest of the neck… and that is determined by whether or not the horse is lifting the front of his ribcage and using the base of his neck to help do that.
For these reasons, it doesn’t matter that we can’t see the head of the horse in the picture. You can infer much of what you need by seeing the back 3/4s of that horse’s body. You can see him squatting and holding the front of his body up. His neck comes out of his shoulder close to the vertical because, it’s biomechanically easier for him to draw that heavy skull hanging out there off the end of his neck in toward his center of gravity, which has rocked up and back from where it usually is.
To consider the problem of how and why a horse is Behind the Vertical or not, compare the positions of his ribcage, to the base of his neck, to his throat latch (open or closed)/his forehead, when he is standing still, if he were the winning hunter at the trot or canter in the hack, and if he were an upper-level dressage horse in collection. When he is standing still, every horse will have his throat latch reasonably open, or as many degrees open as is natural for him, given the shape and orientation of his neck to his shoulder. That varies with the purpose for which the horse has been bred, or course.
While a horse is standing still and when his neck is closer to the “natural degree of horizontalness” his neck was bred for, he is not using quite so much muscular energy to hold his head where it is. Rather, the nuchal ligament is more efficiently doing that mechanical work. The more we (correctly) ask a horse to recruit the muscles in his lower neck, thoracic sling and bas to lift the front of his rib cage, the more we are asking him to use muscle, rather than ligament to hold up his rather heavy skull positioned way out from his center of gravity. It takes time to build that postural strength.
In the correctly-trained horse who is this up-hill, his throat latch will be closed for these biomechanical reasons. The rider will not have pulled the horse’s head in toward his chest. If you see horses ridden in curb bits with loose reins, or horses rearing, notice that they close their throat latches.
A very good hunter in a hack will also raise his ribcage and travel in an “uphill” posture. But he will not be squatting, as is the horse in the picture. Rather, he’s using his hind end to push out, not just up. In this posture and doing that job, his neck comes out of his shoulder a bit up and you can see the muscling of his lower trapezius (ahead of the withers) and crest doing some work. But his throat latch is open because his center of gravity, while higher than it is when he is standing still, has not moved backward significantly. Biomechanically, it follows, he has no reason to close his throat latch and draw his head in.
The money shots:
What people are (rightly) complaining about with the BTV stuff in dressage is a horse whose head has been artificially pulled in for the relatively low- and forward position of his center of gravity. Another way of saying this is that the lower-level horse, ridden with a less extremely uphill and compressed posture is being ridden with his neck held that way.
A third way to put this is that they are using the trying to create an orientation of the ribcage by, in part, controlling the position of the head. And here’s a dirty little secret based on a biomechanical truth: Because the horse uses his heavy skull out at the end of his neck as a counterweight to his hind end, the laws of physics mean that you can influence his posture by controlling where he puts his head. That’s a huge reason for just about every riding discipline out there caring about head, neck and throat latch positions. IMO, the very best, horse-friendly and “purist” horsemen ride to create uphill posture first. The feel and control the body from the shoulders back and let the horse put his head anywhere he finds convenient for the level of collection or extension he’s doing.
The other money shot is that looking at a horse, you should not mistake “superficial” for the “deep.” What counts is the horse’s posture. Learn to see that. The position of the head and neck is follows from that in the horse who has “honest” biomechanics. What you are seeing when you notice something about the head and neck or BTV that doesn’t look right is incongruous biomechanics.
IMO, you are also watching a rider dig a very big training hole for themselves. Or you are seeing a horse who has been ridden that way for so long that he has learned to tuck his chin and leave his back low. That’s a hard problem to fix. That said, a momentary BTV moment in a horse isn’t a problem. Rather, it’s an expression of muscle fatigue in the postural muscles. It should go away as the horse gets stronger in his body and can hold himself in the uphill position (or even more uphill) for longer periods of time. But if I’m riding a horse who gets BTV and stays there, I know I have to give him a break. There is no good muscle to be built with a horse who is continuously cruising around BTV.
Hope this helps.
a whole group of crap lower level dressage trainers and riders whose number one goal even on a green horse is to get the neck “round” meaning BTV and broken at the 3rd vertebrae.